$90$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $86$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 90}$ ${x = 3y-86}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-86}$ for $x$ in the first equation. ${(3y-86)}{+ y = 90}$ Simplify and solve for $y$ $ 3y-86 + y = 90 $ $ 4y-86 = 90 $ $ 4y = 176 $ $ y = \dfrac{176}{4} $ ${y = 44}$ Now that you know ${y = 44}$ , plug it back into ${x = 3y-86}$ to find $x$ ${x = 3}{(44)}{ - 86}$ $x = 132 - 86$ ${x = 46}$ You can also plug ${y = 44}$ into ${x+y = 90}$ and get the same answer for $x$ ${x + }{(44)}{= 90}$ ${x = 46}$ There were $46$ home team fans and $44$ away team fans.